A172224 Number of ways to place 6 nonattacking zebras on a 6 X n board.

1, 924, 8989, 37270, 145233, 525796, 1605490, 4136952, 9435413, 19632414, 37957424, 69050898, 119351315, 197524064, 314935542, 486171662, 729604121, 1068003424, 1529198580, 2146783422, 2960869583, 4018886128, 5376425842

Offset

1,2

Comments

Zebra is a (fairy chess) leaper [2,3].

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Eric Weisstein's World of Mathematics, Zebra Graph

Wikipedia, Zebra (chess)

Formula

a(n) = (1944n^6-27540n^5+227070n^4-1222555n^3+4366071n^2-9580580n+9925860)/30, n>=15.

For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (k-1)(9k-20)/2/k!*(kn)^(k-1) + ...

G.f.: -x * (32*x^20 -48*x^19 -84*x^18 -1004*x^17 +3350*x^16 -802*x^15 +3364*x^14 -32132*x^13 +42540*x^12 +3538*x^11 +10674*x^10 -126767*x^9 +151663*x^8 -20769*x^7 -34421*x^6 +9539*x^5 +40807*x^4 -6284*x^3 +2542*x^2 +917*x +1) / (x-1)^7. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[-(32 x^20 - 48 x^19 - 84 x^18 - 1004 x^17 + 3350 x^16 - 802 x^15 + 3364 x^14 - 32132 x^13 + 42540 x^12 + 3538 x^11 + 10674 x^10 - 126767 x^9 + 151663 x^8 - 20769 x^7 - 34421 x^6 + 9539 x^5 + 40807 x^4 - 6284 x^3 + 2542 x^2 + 917 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Crossrefs

Cf. A061992, A172221, A172222, A172223.

Sequence in context: A024758 A347261 A245859 * A283577 A361608 A177304

Adjacent sequences: A172221 A172222 A172223 * A172225 A172226 A172227

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved